The star of the new movie drama House of Sand and Fog has vaulted onto Hollywood's A-list of leading ladies in recent years for a series of films exploring dark themes.

The 33-year-old actress has played the colleague of a doomed scientist (Hulk), the wife of a schizophrenic mathematics genius (A Beautiful Mind), the mistress of a tortured painter (Pollock), the drug-addicted girlfriend of a junkie (Requiem for a Dream) and the doomed lover of a politician (Waking the Dead).

Things don't get much brighter in Sand and Fog, with her role as Kathy Nicolo, a recovering alcoholic whose home is repossessed by the authorities in lieu of back taxes.

Connelly says she has had enough of tragic heroines, but comedic roles just do not come her way.

"It's not like, you know, the hot new comedy comes around and they think of Jennifer Connelly," she jokes.

Sand and Fog won't help Connelly build a reputation for leaving audiences laughing, but the buzz in Hollywood is that it just might deliver her a second Oscar.

Her first was for supporting actress, playing Alicia Nash, wife of Nobel laureate John Nash, in 2001's A Beautiful Mind.

"It's a bit early, but it's a nice sign people are considering this movie that way," Connelly says.

"Clearly, you do a film and you hope people like it. It's a worthwhile film. It's well-executed, and it's really about something."

The movie, based on a best-selling novel by Andres Dubus, revolves around two people struggling over ownership of a seaside bungalow in northern California.

But for Connelly's Nicolo, it represents more than a home: it's safety and security as she deals with depression and alcoholism.

When the local government auctions it off because she failed to pay a tax bill, she fights to get it back. It is bought by Amir Behrani (Ben Kingsley), a former colonel in the Iranian air force.

Behrani, who has two low-paying jobs to maintain an appearance of wealth and influence in his community of Iranian expatriates and has saved money diligently, buys the bungalow fast. He plans to fix it up and sell it at a profit to restore his own dignity.

Behrani's purchase and Nicolo's inability to reverse it legally sets in motion a chain of events that lead both on a downward spiral of manipulation and deception as they try to outwit each other and the government.

Nicolo also encounters resistance to her pleas for help, given her penniless and homeless state.

Connelly says the movie is "largely about intolerance", and not just ethnic prejudice.

She says Sand and Fog and other recent films, such as Requiem for a Dream, are movies "that just kind of grab you and shake you up a bit".

The actress, who has two sons and is married to actor Paul Bettany (Master and Commander), took a break from films in the late 1990s.

She returned for Waking the Dead and Requiem - both low-budget, art-house films that rekindled her career.

Requiem, in particular, was considered a bold choice because of its subject.

Connelly says she likes the risk involved in projects considered too dangerous for the big studios. "Otherwise, (acting) would just be very boring."

Connelly says her recent characters have been very "emotionally demonstrative", but in her life she can be shy.

The day she won her Oscar, her husband says she had forgotten about the awards until he called to ask if she had prepared her speech. At that point, she didn't have one.

"I've never seen anyone so unconcerned about it," Bettany says. Connelly disagrees, saying that when she's stressed she tends to appear calm even though she is a bundle of nerves.

"I had a bit of the deer-in-the-headlights syndrome (on Oscar night)," she says. "It is an overwhelming moment, a big, big moment."

If Sand and Fog scores as well with Oscar voters as it has with early audiences, she may be able to have another big moment.